Cheryl Grimmer, aged three, was kidnapped from a changing area after spending a morning at the seaside with her mother and three brothers in 1970, near the city of Wollongong in New South Wales (NSW) state.
The body of the child, originally from Bristol, has never been discovered.
Jeremy Buckingham, of the Legalise Cannabis Party, used parliamentary privilege on Thursday to identify a man known as Mercury.
Mercury, who was 16 at the time of the incident, was charged in 2017 with Cheryl’s abduction and murder after police discovered a confession from 1971.
However, key evidence was ruled inadmissible and the charges against him were dropped.
A judge ruled the man’s interview with police from April 1971 could not be used in court because there had been no parent, adult or lawyer accompanying him, Australian media reported at the time.
In parliament on Thursday, Mr Buckingham read out Mercury’s confession and revealed his identity before calling for a new investigation into Cheryl’s murder.
“The family of Cheryl Grimmer have been through so much anguish over such a long period of time,” he said.
“(Mercury) is a free man living with his identity suppressed from his neighbours and no one has been punished for Cheryl Grimmer’s abduction and murder.”
On the 50th anniversary of her disappearance, NSW authorities upped the reward on the cold case to one million Australian dollars (£528,000) for information leading to arrest and conviction.
A coroner in 2011 found Cheryl had died – but her cause and manner of death remained undetermined, NSW Police said.